Recent advances in hardware technology have allowed companies and organizations to automatically and rapidly record transactions of everyday life (e.g., banking, credit card, stock, telecommunications, etc.). The recordation of such processes leads to large amounts of data, which grows at an unlimited rate. The continuous arrival of data is referred to as a data stream. Data streams have been extensively researched in recent years due to their use in a wide range of applications, see, e.g., B. Babcock et al., “Models and Issues in Data Stream Systems,” ACM PODS Conference, 2002; P. Domingos et al., “Mining High-Speed Data Streams,” ACM SIGKDD Conference, 2000; S. Guha et al., “Clustering Data Streams,” IEEE FOCS Conference, 2000; and L. O'Callaghan et al., “Streaming-Data Algorithms For High-Quality Clustering,” ICDE Conference, 2002.
The clustering of a data stream partitions a given set of data points into one or more groups of similar data points. Clustering has been widely researched in the database, data mining and statistics communities, see, e.g., P. Bradley et al., “Scaling Clustering Algorithms to Large Databases,” SIGKDD Conference, 1998; S. Guha et al., “CURE: An Efficient Clustering Algorithm for Large Databases,” ACM SIGMOD Conference, 1998; R. Ng et al., “Efficient and Effective Clustering Methods for Spatial Data Mining,” Very Large Data Bases Conference, 1994; R. Dubes et al., “Algorithms for Clustering Data,” Prentice Hall, New Jersey, 1998; and L. Kaufman et al., “Finding Groups in Data—An Introduction to Cluster Analysis,” Wiley Series in Probability and Math Sciences, 1990. Clustering has also been studied in the context of the data stream environment, see, e.g., S. Guha et al. and L. O'Callaghan et al.
Since the clustering of data streams results in the arrival of a large volume of data, it renders most traditional clustering methodologies inefficient. In recent years, one-pass clustering methodologies have been developed for utilization with data streams. However, the results of a simple one-pass clustering methodology provided over a data stream for a few years would be dominated by the outdated history of the stream.
Other existing methodologies for clustering data streams compute clusters over the entire data stream, see, e.g. L. O'Callaghan et al. These techniques view data stream clustering as a variant of one-pass clustering methodologies. Although such techniques may be useful in many clustering applications, the clustering of data streams requires careful defining in the data stream context. A data stream should be viewed as an infinite process having data that continuously evolves with time. As a result, the underlying clusters may also change considerably with time. The nature of the clusters may vary depending on the moment at which they are computed as well as the time horizon over which they are measured. For example, a user may wish to examine clusters occurring in the last month, year, or decade, each of which may be considerably distinct.
Data streams inherently impose a one-pass constraint on methodology design. It becomes very difficult to provide flexibility in computing clusters over different kinds of time horizons using conventional methodologies. For example, a direct extension of the stream based k-means methodology (see, e.g., L. O'Callaghan et al.) would require simultaneous maintenance of the intermediate results of clustering methodologies over all possible time horizons. Such a computational burden increases with progression of the data stream and can rapidly become a bottleneck for online implementation. Furthermore, in many cases, an analyst may wish to determine the clusters at a previous moment in time, and compare them to the current clusters. This requires even greater bookkeeping, which can rapidly become unwieldy for fast data streams.
Since a data stream cannot be revisited over the course of the computation, a clustering methodology needs to maintain a substantial amount of information so that important details are not lost. For example, a continuous version of k-means methodology maintains a number of cluster centers which change or merge as necessary throughout the execution of the methodology, see, e.g., L. O'Callaghan et al. This approach is unpredictable when the characteristics of the stream evolve over time since the k-means approach is highly sensitive to the order of arrival of the data points. For example, once two cluster centers are merged, there is no way to informatively split the clusters when required by the evolution of the stream at a later time.
A need therefore exists to improve the quality of the clusters when the data evolves considerably over time. A further need exists to provide greater functionality in discovering and exploring clusters over different portions of the stream.